March 18th, 2017, 09:19 PM  #1 
Senior Member Joined: Jan 2017 From: US Posts: 104 Thanks: 5  Algebra, and Graphing, and Functions, and...What??
So, how would you determine if f(x)=x$\displaystyle ^2$1 has a minimum or a maximum? And also, how would you go about graphing it? Sorry if I seem ignorant on the subject; but hey, that's what math forums are for, right? Hehe Thanks in advance! 
March 18th, 2017, 09:27 PM  #2 
Senior Member Joined: Feb 2016 From: Australia Posts: 1,533 Thanks: 513 Math Focus: Yet to find out. 
I think it may help ignore you start by drawing a rough graph to get a feel for the function, then proceed in finding its min/max. Do you know how to draw a graph of a function?

March 18th, 2017, 09:37 PM  #3 
Senior Member Joined: Jan 2017 From: US Posts: 104 Thanks: 5  I am going to be really honest, no I don't. But I would definitely be open to it if you could sum up how to graph a function. I am pretty new to the graphing thing, just getting into that in Algebra. So your help is definitely appreciated!

March 19th, 2017, 12:23 AM  #4 
Global Moderator Joined: Dec 2006 Posts: 18,683 Thanks: 1522 
Do you see why x²  1 can't be greater than 1 if x is real?

March 20th, 2017, 02:12 AM  #5 
Newbie Joined: Mar 2017 From: VietNam Posts: 7 Thanks: 2 
The easiest way is go to desmos.com and type the function! When you look at the graph, you can see what is maximum or minimum (if they exist!) For example, this function f(x)=x^21 has vertex (0;1), and looking at the graph we can see that it has one maximum = 1, and no minimum! Last edited by skipjack; March 20th, 2017 at 02:26 AM. 
March 21st, 2017, 02:56 PM  #6  
Senior Member Joined: Jan 2017 From: US Posts: 104 Thanks: 5  Quote:
 
March 21st, 2017, 04:46 PM  #7  
Senior Member Joined: Aug 2012 Posts: 1,760 Thanks: 480  Quote:
But then I thought ... is that true? If someone is learning algebra today, should they learn to make a twocolumn table, label the columns x and f(x), and plug in numbers by hand? Then plot the points (x, f(x)) on graph paper. This is how you get a visceral feel for the functions. But I do wonder if that's true. I'd love to hear people's opinions about this. When we teach algebra in the modern world, should we make people graph points by hand and only use the calculator as a secondary tool? Or should i just forget about it, get off my dinosaur, and tell the kids, 'There's an app for that!" OP what do you think? Do you understand that the points on the graph are exactly the points (x, f(x)) on the plane? That's the main thing to know.  
March 21st, 2017, 05:10 PM  #8  
Senior Member Joined: May 2016 From: USA Posts: 916 Thanks: 366  Quote:
I still have sitting on my desk Standard Mathematical Tables. I remember when using logarithms was an essential of computations. I know how to use a slide rule, but I think mine is lost. I'd like to see far more reliance on electronic tools in place of mechanical drills and a huge increase in word problems so that students get more experience in deciphering what tools apply to different situations. The main advantage to graph sketching, which really requires differential calculus is that are sure to understand why the graph looks as it does. So I would not eliminate skills such as graph sketching, but I sure would place far less emphasis on it.  
March 21st, 2017, 06:56 PM  #9  
Senior Member Joined: Jan 2017 From: US Posts: 104 Thanks: 5  Quote:
I definitely understand what you're saying, and here's my honest opinion: I think learning to do things without electronic reliance is usually very important, and that trusting your own brain more so than a calculator is a smarter option. I think technology can be a great thing, though maybe we could be using it in some other ways. In general, I don't think the whole "there's an app for that!" stance will get you very far. I also think it's good if you can learn to think for yourself, with some common sense, rather than relying on technology. However, here's my predicament with this: I don't know where you live, but in the US, Common Core is pretty out of hand with math particularly. It isn't about simply solving a problem like a+b anymore you have to go through a set of nonsensical steps (because, you can't just use your brain and add), along with about an essay of a description of why you did what you did, or else you don't points at all (even if your initial answer was correct). And, might I add, the steps they are making everyone go through make no sense, and will never need to be used by anyone in life (unless you become a common core professor or something). In that case, I don't think calculators are such a bad thing, as long as you know how to do the basic math that you will actually use in life. As a student who has been dealing with common core for a while, and can actually think for herself, that is my humble opinion. However, I can definitely see where you're coming from. Last edited by Indigo28; March 21st, 2017 at 07:00 PM.  
March 21st, 2017, 07:15 PM  #10  
Senior Member Joined: Feb 2016 From: Australia Posts: 1,533 Thanks: 513 Math Focus: Yet to find out.  Quote:
I can't... So I can't say for sure what it would have been like to have skipped doing that by hand and instead used software to plot graphs. Last edited by skipjack; March 22nd, 2017 at 12:17 PM.  

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